A261802 - OEIS

%I #16 Aug 21 2024 09:44:02

%S 1,10,155,2320,34640,517252,7723970,115339960,1722340115,25719233330,

%T 384058268507,5735036957760,85639736481880,1278834734405320,

%U 19096488909285540,285162639746429024,4258255614078447290,63587365059302801520,949532710487622388080

%N Number of 10-compositions of n: matrices with 10 rows of nonnegative integers with positive column sums and total element sum n.

%C Also the number of compositions of n where each part i is marked with a word of length i over a denary alphabet whose letters appear in alphabetical order.

%H Alois P. Heinz, <a href="/A261802/b261802.txt">Table of n, a(n) for n = 0..850</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (20, -90, 240, -420, 504, -420, 240, -90, 20, -2).

%F G.f.: (1-x)^10/(2*(1-x)^10-1).

%F a(n) = A261780(n,10).

%F a(n) = Sum_{k>=0} (1/2)^(k+1) * binomial(n-1+10*k,n). - _Seiichi Manyama_, Aug 06 2024

%p a:= proc(n) option remember; `if`(n=0, 1,

%p       add(a(n-j)*binomial(j+9, 9), j=1..n))

%p     end:

%p seq(a(n), n=0..20);

%Y Column k=10 of A261780.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Sep 01 2015